1. Field of the invention
The invention generally relates to the field of signal processing. More specifically the invention is related to efficient mathematical projection of signals for the purpose of signal filtering.
2. Discussion of the Related Art
Signal processing is the process of altering the characteristics of a signal in a desired way or deriving desired parameters from a signal. It is often used in the recovery of transmitted signals. While various forms of analog and digital signal processing exist, digital signal processing has become increasingly popular due to advances in digital processor technologies and the relative ease in operating with quantized representations of signals. Digital signal filtering, in particular, provides a means to mitigate the effects of undesired signals (e.g., noise and/or interference) to more accurately recover a signal.
Digital signal filtering has long been used to separate desired components of a digital signal from undesired signal components. For example, a digital filter may be used to allow frequency components of a desired signal to pass while substantially blocking the frequency components of an undesired signal. In order to efficiently utilize time and frequency in a communication system, multiple access schemes are used to specify how multiple users or multiple signals may share a specified time and frequency allocation. Spread spectrum techniques may be used to allow multiple users and/or signals to share the same frequency band and time simultaneously. Code division multiple access (“CDMA”) is an example of spread spectrum that assigns a unique code to differentiate each signal and/or user. The codes are typically designed to have minimal cross-correlation to mitigate interference. However, even with a small cross-correlation between codes, CDMA is an interference-limited system. Digital signal filters that only pass or block selected frequency bands of a signal to filter out unwanted frequency bands are not applicable since CDMA signals share the same frequency band.
Examples of CDMA communication system include global positioning systems (“GPS”) and CDMA wireless telephony. The multiple access coding schemes specified by standards thereby provide “channelization,” or channel separability, for the system. In a typical CDMA wireless telephony system, a transmitter may transmit a plurality of signals in the same frequency band by using a combination of spreading codes and/or covering codes. For example, each transmitter may be identified by a unique spreading code or spreading code offset. Moreover, a single transmitter may transmit a plurality of signals sharing the same spreading code, but may distinguish between signals with a unique covering code. Covering codes further encode the signal and provide channelization of the signal. Spreading codes and covering codes are known to those skilled in the art.
While certain signaling implementations such as the coding schemes of CDMA have been useful in efficiently utilizing a given frequency band, these coded signals may still interfere with one another. For example, coded signals may interfere due to similarities in codes and associated signal energy. Lack of orthogonality between these signals results in “leakage” from one signal into another. Examples of this leakage include “co-channel” and “cross-channel” interference. Co-channel interference may include multipath interference from the same transmitter, wherein a transmitted signal takes unique paths that causes one path (e.g., an interfering signal path) and another path (e.g., a selected signal path) to differentially arrive at a receiver, thereby hindering reception of the selected signal path. Cross-channel interference may include interference caused by signal paths of other transmitters hindering the reception of the selected signal path.
Interference can degrade communications because interference may cause a receiver to incorrectly recover transmitted data. Interference may also have other deleterious effects on communications. For example, interference may diminish capacity of a communication system, decrease the region of coverage and/or decrease maximum data rates. For these reasons, a reduction in interference may improve signal processing of selected signals while addressing the aforementioned limitations due to interference.
Certain types of projection techniques have been developed which project a received signal onto a subspace orthogonal to a Signal Of Interest (“SOI”) lies. The signal may be decomposed into a component that lies in the subspace containing the interference and an orthogonal subspace. This projection operation determines the amount of the signal that lies in the direction of the SOI. However, residual energy of the interfering components may lie in the direction of the SOI since the interfering signal and the SOI may not be orthogonal. This residual energy may degrade the recovery of the SOI. Projective methods for interference cancellation of a plurality of signals may include a matrix inverse containing non-independent vectors. In software and hardware implementations, a full matrix inverse may be computationally expensive.